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Analysis of a frictional contact problem for viscoelastic materials with long memory
1. | Jagiellonian University, Faculty of Mathematics and Computer Science, Institute of Computer Science, ul. Łojasiewicza 6, 30348 Krakow, Poland, Poland |
2. | Laboratoire de Mathématiques et Physique pour les Systèmes, Université de Perpignan, 52 Avenue Paul Alduy, 66860 Perpignan |
References:
[1] |
F. H. Clarke, "Optimization and Nonsmooth Analysis," Wiley, Interscience, New York, 1983. |
[2] |
Z. Denkowski, S. Migórski and N. S. Papageorgiou, "An Introduction to Nonlinear Analysis: Theory," Kluwer Academic/Plenum Publishers, Boston, Dordrecht, London, New York, 2003. |
[3] |
Z. Denkowski, S. Migórski and N. S. Papageorgiou, "An Introduction to Nonlinear Analysis: Applications," Kluwer Academic/Plenum Publishers, Boston, Dordrecht, London, New York, 2003. |
[4] |
A. D. Drozdov, "Finite Elasticity and Viscoelasticity - A Course in the Nonlinear Mechanics of Solids," World Scientific, Singapore, 1996. |
[5] |
G. Duvaut and J. L. Lions, "Inequalities in Mechanics and Physics," Springer-Verlag, Berlin, 1976. |
[6] |
C. Eck, J. Jarušek and M. Krbec, "Unilateral Contact Problems: Variational Methods and Existence Theorems," Pure and Applied Mathematics, 270, Chapman/CRC Press, New York, 2005. |
[7] |
W. Han and M. Sofonea, "Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity," American Mathematical Society, International Press, 2002. |
[8] |
I. R. Ionescu, C. Dascalu and M. Campillo, Slip-weakening friction on a periodic system of faults: Spectral analysis, Z. Angew. Math. Phys. (ZAMP), 53 (2002), 980-995.
doi: 10.1007/PL00012624. |
[9] |
I. R. Ionescu, Q.-L. Nguyen and S. Wolf, Slip displacement dependent friction in dynamic elasticity, Nonlinear Analysis, 53 (2003), 375-390.
doi: 10.1016/S0362-546X(02)00302-4. |
[10] |
S. Migórski, Hemivariational inequality for a frictional contact problem in elasto-piezoelectricity, Discrete Continuous Dynam. Syst. Ser. B, 6 (2006), 1339-1356.
doi: 10.3934/dcdsb.2006.6.1339. |
[11] |
S. Migórski, A. Ochal and M. Sofonea, Integrodifferential hemivariational inequalities with applications to viscoelastic frictional contact, Mathematical Models and Methods in Applied Sciences, 18 (2008), 271-290.
doi: 10.1142/S021820250800267X. |
[12] |
Z. Naniewicz and P. D. Panagiotopoulos, "Mathematical Theory of Hemivariational Inequalities and Applications," Marcel Dekker, Inc., New York, Basel, Hong Kong, 1995. |
[13] |
P. D. Panagiotopoulos, "Hemivariational Inequalities, Applications in Mechanics and Engineering," Springer-Verlag, Berlin, 1993. |
[14] |
A. D. Rodríguez-Aros, M. Sofonea and J. M. Viaño, A class of evolutionary variational inequalities with Volterra-type integral term, Mathematical Models and Methods in Applied Sciences, 14 (2004), 555-577. |
[15] |
M. Shillor, M. Sofonea and J. J. Telega, "Models and Analysis of Quasistatic Contact," Lecture Notes Physics, 655, Springer, Berlin, Heidelberg, 2004. |
[16] |
M. Sofonea and A. Matei, "Variational Inequalities with Applications. A Study of Antiplane Frictional Contact Problems," Advances in Mechanics and Mathematics, 18, Springer, New York, 2009. |
[17] |
M. Sofonea, A. D. Rodríguez-Aros and J. M. Viaño, A class of integro-differential variational inequalities with applications to viscoelastic contact, Mathematical and Computer Modelling, 41 (2005), 1355-1369.
doi: 10.1016/j.mcm.2004.01.011. |
[18] |
E. Zeidler, "Nonlinear Functional Analysis and Applications II A/B," Springer, New York, 1990. |
show all references
References:
[1] |
F. H. Clarke, "Optimization and Nonsmooth Analysis," Wiley, Interscience, New York, 1983. |
[2] |
Z. Denkowski, S. Migórski and N. S. Papageorgiou, "An Introduction to Nonlinear Analysis: Theory," Kluwer Academic/Plenum Publishers, Boston, Dordrecht, London, New York, 2003. |
[3] |
Z. Denkowski, S. Migórski and N. S. Papageorgiou, "An Introduction to Nonlinear Analysis: Applications," Kluwer Academic/Plenum Publishers, Boston, Dordrecht, London, New York, 2003. |
[4] |
A. D. Drozdov, "Finite Elasticity and Viscoelasticity - A Course in the Nonlinear Mechanics of Solids," World Scientific, Singapore, 1996. |
[5] |
G. Duvaut and J. L. Lions, "Inequalities in Mechanics and Physics," Springer-Verlag, Berlin, 1976. |
[6] |
C. Eck, J. Jarušek and M. Krbec, "Unilateral Contact Problems: Variational Methods and Existence Theorems," Pure and Applied Mathematics, 270, Chapman/CRC Press, New York, 2005. |
[7] |
W. Han and M. Sofonea, "Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity," American Mathematical Society, International Press, 2002. |
[8] |
I. R. Ionescu, C. Dascalu and M. Campillo, Slip-weakening friction on a periodic system of faults: Spectral analysis, Z. Angew. Math. Phys. (ZAMP), 53 (2002), 980-995.
doi: 10.1007/PL00012624. |
[9] |
I. R. Ionescu, Q.-L. Nguyen and S. Wolf, Slip displacement dependent friction in dynamic elasticity, Nonlinear Analysis, 53 (2003), 375-390.
doi: 10.1016/S0362-546X(02)00302-4. |
[10] |
S. Migórski, Hemivariational inequality for a frictional contact problem in elasto-piezoelectricity, Discrete Continuous Dynam. Syst. Ser. B, 6 (2006), 1339-1356.
doi: 10.3934/dcdsb.2006.6.1339. |
[11] |
S. Migórski, A. Ochal and M. Sofonea, Integrodifferential hemivariational inequalities with applications to viscoelastic frictional contact, Mathematical Models and Methods in Applied Sciences, 18 (2008), 271-290.
doi: 10.1142/S021820250800267X. |
[12] |
Z. Naniewicz and P. D. Panagiotopoulos, "Mathematical Theory of Hemivariational Inequalities and Applications," Marcel Dekker, Inc., New York, Basel, Hong Kong, 1995. |
[13] |
P. D. Panagiotopoulos, "Hemivariational Inequalities, Applications in Mechanics and Engineering," Springer-Verlag, Berlin, 1993. |
[14] |
A. D. Rodríguez-Aros, M. Sofonea and J. M. Viaño, A class of evolutionary variational inequalities with Volterra-type integral term, Mathematical Models and Methods in Applied Sciences, 14 (2004), 555-577. |
[15] |
M. Shillor, M. Sofonea and J. J. Telega, "Models and Analysis of Quasistatic Contact," Lecture Notes Physics, 655, Springer, Berlin, Heidelberg, 2004. |
[16] |
M. Sofonea and A. Matei, "Variational Inequalities with Applications. A Study of Antiplane Frictional Contact Problems," Advances in Mechanics and Mathematics, 18, Springer, New York, 2009. |
[17] |
M. Sofonea, A. D. Rodríguez-Aros and J. M. Viaño, A class of integro-differential variational inequalities with applications to viscoelastic contact, Mathematical and Computer Modelling, 41 (2005), 1355-1369.
doi: 10.1016/j.mcm.2004.01.011. |
[18] |
E. Zeidler, "Nonlinear Functional Analysis and Applications II A/B," Springer, New York, 1990. |
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